53,917 research outputs found
Paired and Total Domination on the Queen\u27s Graph.
The Queen’s domination problem has a long and rich history. The problem can be simply stated as: What is the minimum number of queens that can be placed on a chessboard so that all squares are attacked or occupied by a queen? The problem has been expanded to include not only the standard 8x8 board, but any rectangular m×n sized board. In this thesis, we consider both paired and total domination versions of this renowned problem
Complexity of Chess Domination Problems
We study different domination problems of attacking and non-attacking rooks
and queens on polyominoes and polycubes of all dimensions. Our main result
proves that maximal domination is NP-complete for non-attacking queens and for
non-attacking rooks on polycubes of dimension three and higher. We also analyse
these problems for polyominoes and convex polyominoes, conjecture the
complexity classes and provide a computer tool for investigation. We have also
computed new values for classical queen domination problems on chessboards
(square polyominoes). For our computations, we have translated the problem into
an integer linear programming instance. Finally, using this computational
implementation and the game engine Godot, we have developed a video game of
minimal domination of queens and rooks on randomly generated polyominoes.Comment: 19 pages, 20 figures, 4 tables. Theorem 1 now for d>2, added results
on approximation, fixed typos, reorganised some proof
Queen\u27s domination using border squares and (\u3ci\u3eA\u3c/i\u3e,\u3ci\u3eB\u3c/i\u3e)-restricted domination
In this paper we introduce a variant on the long studied, highly entertaining, and very difficult problem of determining the domination number of the queen\u27s chessboard graph, that is, determining how few queens are needed to protect all of the squares of a k by k chessboard. Motivated by the problem of minimum redundance domination, we consider the problem of determining how few queens restricted to squares on the border can be used to protect the entire chessboard. We give exact values of border-queens required for the k by k chessboard when 1≤k≤13. For the general case, we present a lower bound of k(2-9/2k-√(8k2-49k+49)/2k) and an upper bound of k-2. For k=3t+1 we improve the upper bound to 2t+1 if 3t+1 is odd and 2t if 3t+1 is even.
We generalize this problem to (A,B)-restricted parameters for vertex subsets A and B of V(G) where, for example, one must use only vertices in A to dominate all of B. Defining upper and lower parameters for independence, domination, and irredundance, we present a generalization of the domination chain of inequalities relating these parameters
THE DOMINANCE OF CLAN REFLECTED IN VICTORIA AVEYARD’S RED QUEEN (2015): A SOCIOLOGICAL APPROACH
This study discusses the dominance of a clan in the Red Queen novel by Victoria Aveyard and uses sociology theory in literature. The purpose of this study was to identify indicators of dominance of a clan, describe how depictions of a clan dominate, and reveal the reason the author discusses clan domination in the Red Queen novel. In qualitative descriptive, there are two data used for research. First is the Red Queen novel by Victoria Aveyard as the main data, then the supporting or secondary data includes books, online journals, articles, and internet. The sresult of this research shows two indicators, namely social discrimination which results in clan domination and oppression by the dominating people. The two indicators are described by the author through characters and the setting of the story. This research also shows the results that Victoria Aveyard as the author was inspired by several cases that occurred in the United States. The caseswhich is caused by clan domination, namely racism between black and white skin, and then the problem of attack on 11 September 2001 which resulted in all Muslim worlds being considered terrorists
Sketched Answer Set Programming
Answer Set Programming (ASP) is a powerful modeling formalism for
combinatorial problems. However, writing ASP models is not trivial. We propose
a novel method, called Sketched Answer Set Programming (SkASP), aiming at
supporting the user in resolving this issue. The user writes an ASP program
while marking uncertain parts open with question marks. In addition, the user
provides a number of positive and negative examples of the desired program
behaviour. The sketched model is rewritten into another ASP program, which is
solved by traditional methods. As a result, the user obtains a functional and
reusable ASP program modelling her problem. We evaluate our approach on 21 well
known puzzles and combinatorial problems inspired by Karp's 21 NP-complete
problems and demonstrate a use-case for a database application based on ASP.Comment: 15 pages, 11 figures; to appear in ICTAI 201
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